The Rossoneri had won just one of their prior seven games in all competitions, but they edged a dull affair in Modena as Romagnoli netted a scrappy first-half opener before Suso's sublime second clinched the points.
Although this was far from a vintage display from Montella's men, it was the result that mattered as speculation continues to surround the 43-year-old's future at San Siro - Antonio Conte and Carlo Ancelotti two names that will not go away as the club reportedly seek potential successors.
Having started the game 12 points off the UEFA Champions League places, Milan and Montella could ill afford a slip-up and the coach must have felt a sense of relief when Romagnoli met Hakan Calhanoglu's deflected delivery to score shortly before the interval.
Andrea Consigli had kept the visitors at bay up to that point and he impressed again after the restart until Suso struck to end home hopes of a result.
After consecutive away league wins, Milan have not lost sight of the European spots yet as they move up to seventh.
Consigli made a good early stop from Calhanoglu's curling free-kick, before Montella's latest blow arrived in the form of an ankle injury for Davide Calabria.
As Milan reshuffled, Sassuolo assumed control of the contest and Gianluigi Donnarumma had to be alert to get down to Luca Mazzitelli's low strike.
While the Rossoneri steadily grew into the game, there was an evident lack of quality in both sides' play with a Fabio Borini blast from 20 yards causing Consigli little trouble.
Seven minutes before half-time, though, Franck Kessie finally ignited the visiting attack as he jinked free on the right to centre for a Nikola Kalinic header that Consigli saved instinctively.
The consequent corner would provide the breakthrough and the goalkeeper looked rather less accomplished as he fell cheaply under the challenge of Romagnoli, with referee Antonio Damato wisely rejecting appeals for a foul as the Milan defender nodded into the net.
Montella's men made a slow start to the second half, as they had the first, before building some momentum as the hour-mark approached.
Kessie shimmed onto his left to shoot straight at Consigli and the same man then charged through the midfield to test the keeper again with a stinging drive shortly afterwards.
Suso put the game beyond Sassuolo with 23 minutes remaining, the Spaniard taking possession on the right flank, cutting inside and moving past Federico Peluso before ripping a finish into the top-left corner.
Milan kept pushing, but Kalinic could not stretch to direct a volley on target as Suso delivered a teasing ball and substitute Manuel Locatelli drew only a simple save from Consigli before the visitors saw out the final minutes without major concern.